Some generalizations of the Hadamard expansion for the modified Bessel function Original Research Article

A remarkable result (which is of considerable theoretical importance) is the celebrated Hadamard expansion for the modified Bessel function Iv(z) in a (convergent) series of the incomplete Gamma function γ(α,z). The main object of the present paper is to show how readily this Hadamard expansion can be deduced by suitably specializing much more general bilateral expansions associated with multivariable hypergeometric functions. Several other closely related results are also considered briefly.